Inversion from different kinds of information and real inversion formulas of the Laplace transform from a finite number of data
Abstract
We propose a new method to obtain solutions (and generalized solutions) of general bounded linear operator equations with a parameter on Hilbert spaces. This will be done by using reproducing kernel Hilbert spaces, and some of their properties. As a result of the method, we shall propose a principle to obtain an optimal and natural inverse from only a finite number of given data. In addition, as a prototype example, we shall give new real inversion formulas of the Laplace transform.
Published
2010-05-25
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Section
Articles